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.IX Title "Math::GSL::Chebyshev 3pm"
.TH Math::GSL::Chebyshev 3pm 2024-03-07 "perl v5.38.2" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
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.nh
.SH NAME
Math::GSL::Chebyshev \- Univariate Chebyshev Series Approximation
.SH SYNOPSIS
.IX Header "SYNOPSIS"
.Vb 1
\&    use Math::GSL::Chebyshev qw/:all/;
\&
\&    my $cheb             = gsl_cheb_alloc(40);
\&    my $function         = sub { sin(cos($_[0])) };
\&
\&    gsl_cheb_init($cheb, $function, 0, 10);
\&
\&    my $x                = gsl_cheb_eval($cheb, 5.5 );
\&    my ($status,$y,$err) = gsl_cheb_eval_err($cheb, 7.5 );
\&    gsl_cheb_free($cheb);
.Ve
.SH DESCRIPTION
.IX Header "DESCRIPTION"
.IP \(bu 4
\&\f(CWgsl_cheb_alloc($size)\fR
.Sp
.Vb 1
\&    my $cheb = gsl_cheb_alloc(50);
.Ve
.Sp
Allocates a new Chebyshev object with \f(CW$size\fR sample points.
.IP \(bu 4
\&\f(CWgsl_cheb_free($cheb)\fR
.Sp
Deallocates memory associated to \f(CW$cheb\fR. Returns void.
.IP \(bu 4
\&\f(CW\*(C`gsl_cheb_init($cheb,$function, $lower, $upper)\*(C'\fR
.Sp
.Vb 1
\&    gsl_cheb_init($cheb, sub { sin(cos($_[0])) }, 0, 10 );
.Ve
.Sp
Initiate a Chebyshev object with a function and upper and lower bounds.
Returns void.
.IP \(bu 4
\&\f(CW\*(C`gsl_cheb_eval($function, $value)\*(C'\fR
.Sp
.Vb 1
\&    my $evaluated = gsl_cheb_eval($cheb, 5 );
.Ve
.Sp
Returns a Perl scalar of the Chebyshev object \f(CW$cheb\fR evaluated at \f(CW$value\fR.
.IP \(bu 4
\&\f(CW\*(C`gsl_cheb_eval_err($cheb, $value)\*(C'\fR
.Sp
.Vb 1
\&    my ($status,$evaluated,$err) = gsl_cheb_eval($cheb, 5 );
.Ve
.Sp
Returns a list consisting of a GSL status code, the evaluate value and
the estimated error of the evaluation.
.IP \(bu 4
\&\f(CW\*(C`gsl_cheb_eval_n \*(C'\fR
.IP \(bu 4
\&\f(CW\*(C`gsl_cheb_eval_n_err \*(C'\fR
.IP \(bu 4
\&\f(CW\*(C`gsl_cheb_eval_mode \*(C'\fR
.IP \(bu 4
\&\f(CW\*(C`gsl_cheb_eval_mode_e \*(C'\fR
.IP \(bu 4
\&\f(CW\*(C`gsl_cheb_calc_deriv($deriv,$cheb) \*(C'\fR
.Sp
.Vb 1
\&   my $status = gsl_cheb_calc_deriv( $deriv, $cheb );
.Ve
.Sp
This will calculate the derivative of \f(CW$cheb\fR and stores it
in \f(CW$deriv\fR, which must be pre-allocated. Returns a GSL status code.
.IP \(bu 4
\&\f(CW\*(C`gsl_cheb_calc_integ($integ,$cheb) \*(C'\fR
.Sp
.Vb 1
\&   my $status = gsl_cheb_calc_integ( $deriv, $cheb );
.Ve
.Sp
This will calculate the derivative of \f(CW$cheb\fR and stores it
in \f(CW$deriv\fR, which must be pre-allocated. Returns a GSL status code.
.PP
For more information on the functions, we refer you to the GSL official
documentation: <http://www.gnu.org/software/gsl/manual/html_node/>
.SH AUTHORS
.IX Header "AUTHORS"
Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
.SH "COPYRIGHT AND LICENSE"
.IX Header "COPYRIGHT AND LICENSE"
Copyright (C) 2008\-2023 Jonathan "Duke" Leto and Thierry Moisan
.PP
This program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.